The growth kinetics involved in the selective molecular beam epitaxy growth of GaAs quantum wires (QWRs) on mesa-patterned substrates is investigated in detail experimentally, and an attempt is made to model the growth theoretically, using a phenomenological continuum model. Experimentally, <-110 >-oriented QWRs were grown on (001) and (113)A substrates, and <-1-12 >-oriented QWRs were grown on (I I I)B substrates. From a detailed investigation of the growth profiles, it was found that the lateral wire width is determined by facet boundaries (FBs) within AlGaAs layers separating growth regions on top facets from those on side facets of mesa structures. Evolution of FBs during growth was complicated. For computer simulation, measured growth rates of various facets were fitted into a theoretical formula to determine the dependence of a lifetime of adatoms on the slope angle of the growing surface. The continuum model using the slope angle dependent lifetime reproduced the details of the experimentally observed growth profiles very well for growth on (001), (113)A, and (111)B substrates, including the complex evolution of facet boundaries (c) 2005 American Vacuum Society.